Vibration in vacuum. What would happen?

Main Question or Discussion Point

Place a guitar floating in the vacuum. Once one string start to vibrate it would not stop since there is no air and contact. So any object vibrating in the vacuum would continue to vibrate indefinitely or the energy would become heat and radiation?

It wouldn't vibrate indefinitely - quite a bit of the energy would be dissipated in the string itself. The string is not perfectly elastic, and the mounting points on both ends are not perfectly rigid, so the string would indeed slow down and stop.

As cjl said, some of the energy will be converted into heat inside the string itself. For steel strings this would happen very slowly, but it would be faster for nylon strings. No material is perfectly elastic, and if you measured the force and displacement very accurately, you would see that the graph when the force decreases does not lie exactly on top of the graph when the force increases. In fact, the (small) area between the two curves is a measure of the amount of mechanical energy that is "lost" and converted to heat.

Another (and probably quicker) way that the energy would be turned into heat is by friction. The vibrating strings move slightly backwards and forwards over the bridge and the top of the fingerboard with each cycle of vibration, The joints between the different parts of the guitar body will also move slightly relative to each other, etc, and everywhere this happens there will be a friction force that does work and generates heat.

All those effects are also happening when the guitar is not in a vacuum, of course. You may have assumed that all the energy in the string was converted into sound energy but I bet you never did an experiment to measure whether that was a good assumption. (It would be quite a difficult experiment to measure this accurately, though)